Injective Envelopes and Projective Covers of Quivers
Will Grilliette

TL;DR
This paper characterizes injective and projective objects in the category of quivers and constructs their injective envelopes and projective covers, advancing the understanding of categorical structures in graph theory.
Contribution
It provides explicit characterizations and constructions of injective envelopes and projective covers for quivers, a novel contribution in categorical graph theory.
Findings
Explicit descriptions of injective objects in quivers
Explicit descriptions of projective objects in quivers
Constructed injective envelopes and projective covers for any quiver
Abstract
This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Topological and Geometric Data Analysis
